• Corpus ID: 235359010

Data-driven discovery of interacting particle systems using Gaussian processes

  title={Data-driven discovery of interacting particle systems using Gaussian processes},
  author={Jinchao Feng and Yunxiang Ren and Sui Tang},
Interacting particle or agent systems that display a rich variety of collection motions are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and collective behaviors. In this paper, we study the data-driven discovery of distance-based interaction laws in second-order interacting particle systems. We propose a learning approach that models the latent interaction kernel functions as Gaussian processes, which… 

Figures and Tables from this paper

Learning Mean-Field Equations from Particle Data Using WSINDy
Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
Motivated by the success of IPS models to describe the spatial movement of organisms, WSINDy for second order IPSs to model the movement of communities of cells is developed, motivated by common cell migration experiments.
Scalable marginalization of latent variables for correlated data
This work introduces Gaussian processes (GPs) for modeling correlated data and highlights the computational challenge, where the computational complexity increases cubically fast along with the number of observations, and introduces a novel marginalization technique to estimate interaction kernels and to forecast particle trajectories.


Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems
A very general second-order, heterogeneous, multivariable, interacting agent model, with an environment, that encompasses a wide variety of known systems, and an inference framework that uses nonparametric regression and approximation theory based techniques to efficiently derive estimators of the interaction kernels which drive these dynamical systems.
Data-driven Discovery of Emergent Behaviors in Collective Dynamics
Gaussian Process Assisted Active Learning of Physical Laws
An active learning approach to estimate the unknown differential equations accurately with reduced experimental data size and an adaptive design criterion combining the D-optimality and the maximin space-filling criterion are proposed.
Coarse-scale PDEs from fine-scale observations via machine learning
A data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine-learning algorithms using Gaussian processes, artificial neural networks, and/or diffusion maps is introduced.
Nonlocal Flocking Dynamics: Learning the Fractional Order of PDEs from Particle Simulations
The proposed method offers new insights on how to scale the discrete agent-based models to the continuum-based PDE models, and could serve as a paradigm on extracting effective governing equations for nonlocal flocking dynamics directly from particle trajectories.
Gaussian Process Approximations of Stochastic Differential Equations
A novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations is presented, and the results are very promising as the variational approximate solution outperforms standardGaussian process regression for non-Gaussian Markov processes.
Optimal Rates for Regularization of Statistical Inverse Learning Problems
Strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions are obtained.
Non-asymptotic Analysis in Kernel Ridge Regression
A general non-asymptotic analysis of learning rates in kernel ridge regression (KRR), applicable for arbitrary Mercer kernels with multi-dimensional support, with remarkable extensibility to various inferential goals through augmenting results.
Inferring individual rules from collective behavior
It is found that important features of observed flocking surf scoters can be accounted for by zonal models with specific, well-defined rules of interaction, including strong short-range repulsion, intermediate-range alignment, and longer-range attraction.